CHAPTER 6 EXERCISES AND PROBLEMS Solutions EXERCISE 6-24 (15 MINUTES) 1. Cost per Broadcast Hour July September Cost Item Production crew: $4,875/390 hr. ............................................ $8,000/640 hr. ............................................ Supervisory employees: $5,000/390 hr. ............................................ $5,000/640 hr. ............................................ $12.50 per hr. $12.50 per hr. 12.82 per hr.* 7.81 per hr.* *Rounded. 2. December cost predictions: Production crew (420 $12.50 per hr.).............................................. Supervisory employees....................................................................... $5,250 5,000 3. Cost Item Production crew ......................................................... Supervisory employees ($5,000/420 hr.) ................. Cost per Broadcast Hour in December $12.50 per hr. 11.90 per hr.* *Rounded. EXERCISE 6-25 (15 MINUTES) 1. Variable cost per pint of applesauce produced = $24,100 $22,100 $.10 41,000 21,000 Total cost at 41,000 pints ............................................................................ Variable cost at 41,000 pints (41,000 $.10 per pint) ...................................................................... Fixed cost ..................................................................................................... 6-1 $24,100 4,100 $20,000 Cost equation: Total energy cost = $20,000 + $.10X, where X denotes pints of applesauce produced 2. Cost prediction when 26,000 pints of applesauce are produced Energy cost = $20,000 + ($.10)(26,000) = $22,600 EXERCISE 6-26 (30 MINUTES) 1. Scatter diagram and visually-fitted line: 6-2 Monthly energy cost $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 10,000 20,000 30,000 6-3 40,000 50,000 Pints of apple sauce produced EXERCISE 6-26 (CONTINUED) 2. Answers will vary on this requirement because of variation in the visually-fitted lines. Based on the preceding plot, the cost prediction at 26,000 pounds is: Energy cost = $22,600 3. The July cost observation at the 40,000-pint activity level appears to be an outlier. The cost analyst should check the observation data for accuracy. If the data are accurate, the outlier should be ignored in making cost predictions. EXERCISE 6-29 (15 MINUTES) 1. 2. a. Fixed b. Variable c. Variable d. Fixed e. Semivariable (or mixed) Production cost per month = $33,000* + $2.00X † *33,000 = $19,000 + $10,000 + $4,000 †$2.00 = $1.10 + $.70 + $.20 EXERCISE 6-30 (15 MINUTES) 1. Variable maintenance cost per tour mile = (12,500r-11,000r) / (20,000 miles – 8,000 miles) = .125r r denotes the real, Brazil’s national currency. Total maintenance cost at 8,000 miles ........................................................ Variable maintenance cost at 8,000 miles (.125r 8,000) ......................... Fixed maintenance cost per month ............................................................. 6-4 11,000r 1,000r 10,000r 2. Cost formula: Total maintenance cost per month = 10,000r + .125rX , where X denotes tour miles traveled during the month. 3. Cost prediction at the 22,000-mile activity level: Maintenance cost = 10,000r + (.125r)(22,000) = 12,750r SOLUTIONS TO PROBLEMS PROBLEM 6-36 (25 MINUTES) 1. Machine supplies: $102,000 34,000 direct-labor hours = $3 per hour January: 23,000 direct-labor hours x $3 = $69,000 Depreciation: Fixed at $15,000 2. Plant maintenance cost: Total cost*…………………….. Less: Machine supplies……. Depreciation………….. Plant maintenance…………... March January (34,000 hrs) (23,000 hrs) $ 586,000 (102,000) (15,000) $ 469,000 $ 454,000 (69,000) (15,000) $ 370,000 * Excludes supervisory labor cost Variable maintenance cost = difference in cost difference in direct-labor hours = ($469,000 – $370,000) (34,000 – 23,000) = $99,000 11,000 hours = $9 per hour Fixed maintenance cost: March January (34,000 hrs) (23,000 hrs) Total maintenance cost………………. Less: Variable cost at $9 per hour…. Fixed maintenance cost……………… 6-5 $469,000 306,000 $163,000 $370,000 207,000 $163,000 3. Manufacturing overhead at 29,500 labor hours: Machine supplies at $3 per hour……. $ 88,500 Depreciation……………………………. 15,000 Plant maintenance cost: Variable at $9 per hour…………… 265,500 Fixed…………………………………. 163,000 Supervisory labor……………………… 90,000 Total…………………………….. $622,000 4. A fixed cost remains constant when a change occurs in the cost driver (or activity base). A step-fixed cost, on the other hand, remains constant within a range but will change (rise or fall) when activity falls outside that range. A fixed cost is constant over a much larger range of activity than is a step-fixed cost. 5. Ideally, the company should operate on the right-most portion of a step, just prior to the jump in cost. In this manner, a firm receives maximum benefit (i.e., the maximum amount of activity) for the dollars invested. PROBLEM 6-38 (25 MINUTES) 1 Variable maintenance cost per hour of service . = $4,470 $2,820 520 300 = $7.50 Total maintenance cost at 300 hours of service......................................... Variable maintenance cost at 300 hours of service (300 hr. $7.50) ...... Fixed maintenance cost per month ............................................................. Cost formula: Monthly maintenance cost = $570 + $7.50X, where X denotes hours of maintenance service. PROBLEM 6-38 (CONTINUED) 2 The variable component of the maintenance cost is $7.50 per hour of . service. 3 Cost prediction at 590 hours of activity: . 6-6 $2,820 2,250 $ 570 Maintenance cost = $570 + ($7.50)(590) = $4,995 4 Variable cost per hour [from requirement (2)] ............................................ . Fixed cost per hour at 600 hours of activity ($570/600) ............................. $7.50 $ .95 The fixed cost per hour is a misleading amount, because it will change as the number of hours changes. For example, at 500 hours of maintenance service, the fixed cost per hour is $1.14 ($570/500 hours). PROBLEM 6-43 (25 MINUTES) 1. Scatter diagrams: Present, in graphic form, the relationship between costs and cost drivers via a plot of data points Require that a straight line be fit through the data points, with approximately the same number of data points above and below the line Easy to use Provide a means to easily recognize outliers Least-squares regression: Uses statistical formulas to fit a cost line through the data points Is a very objective method of cost estimation that uses all the data points Requires more computation than other cost-estimation methods; however, software programs are readily available High-low method: Relies on only two data points (for the highest and lowest activity levels) in drawing conclusions about cost behavior Is considered more objective than the scatter diagram; however, is weaker than the scatter diagram because it relies on only two data points The least-squares regression method will typically produce the most accurate results. 2. Yes. The three methods produce equations by different means. Scatter diagrams and least-squares regression rely on an examination of all data points. The scatter diagram, however, requires an analyst to fit a line through the points by visual approximation, or “eyeballing.” In contrast, least-squares regression involves the 6-7 use of statistical formulas to derive the best possible fit of the line through the points. Finally, the high-low method is based on an analysis of only two data points: the highest and the lowest activity levels. 3. These amounts represent the fixed and variable cost associated with the ticketing operation. Fixed cost totals $312,000 within the relevant range, and Global American incurs $2.30 of variable cost for each ticket issued. 4. C = $320,000 + $2.15PT C = $320,000 + ($2.15 x 580,000) C = $1,567,000 5. Yes, she did err by including November data. November is not representative because of the effects of the Delta Western strike. The month is an outlier and should be eliminated from the data set. 6. Currently, most of the airline’s tickets are written through reservations personnel, whose wages are likely variable in nature. Heavier reliance on the Internet means a greater investment in software, Web-site maintenance and development, and other similar expenditures. Outlays that fall in these latter categories are typically fixed costs, assuming that the cost driver is the number of tickets. The outcome would parallel the experiences of a manufacturing firm that automates its processes and reduces its reliance on direct-labor personnel. PROBLEM 6-44 (35 MINUTES) 1. The regression equation's intercept on the vertical axis is $200. It represents the portion of indirect material cost that does not vary with machine hours when operating within the relevant range. The slope of the regression line is $4 per machine hour. For every machine hour, $4 of indirect material costs are expected to be incurred. 2. Estimated cost of indirect material at 900 machine hours of activity: S = $200 + ($4 900) 3. = $3,800 Several questions should be asked: 6-8 (a) Do the observations contain any outliers, or are they all representative of normal operations? (b) Are there any mismatched time periods in the data? Are all of the indirect material cost observations matched properly with the machine hour observations? (c) Are there any allocated costs included in the indirect material cost data? (d) Are the cost data affected by inflation? 4. Beginning inventory ............................................................. + Purchases ........................................................................... – Ending inventory................................................................ Indirect material used ........................................................... 5. April $1,200 6,000 (1,550) $5,650 August $ 950 6,100 (2,900) $4,150 High-low method: Variable cost per machine hour = difference in cost levels difference in activity levels $5,650 $4,150 $1,500 $5 per machine hour 1,100 800 300 Fixed cost per month: = Total cost at 1,100 hours ................................................................................ Variable cost at 1,100 hours ($5 1,100) ............................................................................................... Fixed cost ........................................................................................................ $5,650 5,500 $ 150 Equation form: Indirect material cost = $150 + ($5 machine hours) 6. The regression estimate should be recommended because it uses all of the data, not just two pairs of observations when developing the cost equation. 6-9